This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 8 years ago.
I'm running the following javascript code:
var var1 = 0.53;
var var2 = 0.47;
alert(var1-var2);
This code return:
0.06000000000000005
But if I execute this javascript code:
var var1 = 0.14;
var var2 = 100;
alert(var1*var2);
The return is:
14.0600000000000002
What documentation to explain this?
Thanks!
This is a very fundamental problem that is related to the way floating point numbers are represented (see the wikipedia article for a detailed explanation). It is not specific to javascript.
Since a computer works only on binary values it is not possible to exactly represent certain fractions. Example: 1/2 or 3/4 can be exactly represented. 1/3 on the other hand cannot (like in the decimal system). It is counterintutive that a seemingly "simple" number like 0.14 leads to a rounding error, however, when you think about it as 7/50 = 7/(5 * 5 * 2) it becomes clear. The problem are the fives. 1/5 = 0.2 is nice in the decimal system but not as a binary number.
Update:
I don't mean to say it is not possible to do such kinds of calculations exactly. However, you will have to use certain libraries for this purpose (e.g. for working with currency values)
Related
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 7 years ago.
I am pretty new in JavaScript and I have found a very strange situation doing an extremely simple mathematical operation: a subtraction.
So in a jQuery function I have this code:
saldoRicalcolato = finanziamento - variazioneAnticipoNumber;
Where finanziamento and variazioneAnticipoNumber are 2 numbers having decimal digits.
It works almost always good except for some specific values.
You can replicate the strange behavior performing this statement into the FireBug console:
2205.88 - 1103.01
1102.8700000000001
So in this case the result is substantially wrong because I obtain 1102.8700000000001 and not 1102.87 as I expected.
Why? What am I missing? Is it a JavaScript engine bug or something like this? Possible?
It's not a JavaScript problem but a more general computer problem. Floating number can't store all decimal numbers properly, because they store stuff in binary For example:
0.5 is store as b0.1
but 0.1 = 1/10 so it's 1/16 + (1/10-1/16) = 1/16 + 0.0375
0.0375 = 1/32 + (0.0375-1/32) = 1/32 + 00625 ... etc
so in binary 0.1 is 0.00011...
but that's endless. Except the computer has to stop at some point. So if in our example we stop at 0.00011 we have 0.09375 instead of 0.1.
It doesn't depend on which language but on the computer, what depends on the language is how you display the numbers. Usually the language will round numbers to an acceptable representation but apparently JavaScript doesn't.
If you're looking to get 1102.87. You'll need to set the decimal place to 2 by using toFixed()
This is just a solution of getting the number you want.
alert((2205.88 - 1103.01).toFixed(2));
This question already has answers here:
Closed 12 years ago.
Possible Duplicate:
Is JavaScript's Math broken?
<html>
<body>
<script type="text/javascript">
var w = 0;
var weight1 = parseFloat("0.6");
var weight2 = parseFloat("0.3");
w = weight1 + weight2;
document.write("total weight: " + w);
</script>
</body>
</html>
Why does this print 0.8999999999999999 and not 0.90000000
Because the number 9/10 cannot be represented cleanly in base 2, just like the number 1/3 cannot be cleanly represented in base 10.
Source of the problem:
http://support.microsoft.com/kb/42980
Workarounds:
Is there a definitive solution to javascript floating-point errors?
How to deal with floating point number precision in JavaScript?
http://bytes.com/topic/javascript/answers/682011-solution-floating-point-errors
The way floating point numbers are made, certain values cannot be accurately represented. This is a limitation of this data type, there is little to nothing you can do to fix it, you have to just anticipate this, and make use of round or something.
http://en.wikipedia.org/wiki/Floating_point
Simple rounding errors. floating point numbers are not precise. This makes comparisons a little more complicated. Eg. If (my_float == 3.0) will invariably fail.
To answer your question - floating points have as much precision as your RAM can allow. If you create a floating number 1 - it may actually be 1.000000000000000000001
Obviously your solutions include rounding the number, or using ints
This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 9 years ago.
This kind of blows my mind..
http://pastebin.com/Q3MtpPpM
Turns out the output is "surprise!!". Doesn't this sort of undermine using JavaScript in some way if a program was going to use lots of floating point values?
One way of comparing floats could be by converting them to String values using toFixed() method
var fl1 = 0.11;
var fl2 = 0.11;
if ( fl1.toFixed(10) == fl2.toFixed(10) )
{
//same value
}
Javascript numbers are 64 bit floating point. see this ECMAScript specification.
http://www.ecma-international.org/ecma-262/5.1/#sec-4.3.19
Floating point arithmetic in any programming language is prone to errors and is not always guaranteed to be accurate. see following for more on Floating point airthmatic
http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
for more see the following QA
Is floating point math broken?
And yes its a WAT, but following rules can help you avoid errors
dont do equality checks
in case of critical floats where you know maximum points after denomination for example currency store multiplied value by that base.
for currency store in cents instead of dollors.
54.67 as 5467 --- and divide by 100 before display.
For more read following post (its for c++ but will give insights on floating point erros)
http://www.codeproject.com/Articles/29637/Five-Tips-for-Floating-Point-Programming
This question already has answers here:
Closed 10 years ago.
Possible Duplicate:
Is JavaScript’s Floating-Point Math Broken?
In Javascript, how do I compute the result of 23668-23671.88 to -3.88 instead of -3.8800000000010186 ?
I don't want any rounding, since if I use a windows calc, the result is -3.88.
Is it possible?
If you don't want to round, then you need some way of determining the precision of the variables in your expression and apply that precision to the result of the expression. Unfortunately, JavaScript does not have a way to determine the precision of floats.
However, there is a simple 'hacky' way you can accomplish this:
http://jsfiddle.net/SjxCY/2/
var num = 2.383;
var precision = (num+'').split('.')[1].length;
var final = (234234-num).toFixed(precision);
alert(final);
It's not pretty, but it works.
If you don't want a rounding kludge, you cannot use floating point numbers and have to find a decimal arithmetic library. Nothing built-in, I am afraid.
This question already has answers here:
Closed 12 years ago.
Possible Duplicate:
Is JavaScript's Math broken?
<html>
<body>
<script type="text/javascript">
var w = 0;
var weight1 = parseFloat("0.6");
var weight2 = parseFloat("0.3");
w = weight1 + weight2;
document.write("total weight: " + w);
</script>
</body>
</html>
Why does this print 0.8999999999999999 and not 0.90000000
Because the number 9/10 cannot be represented cleanly in base 2, just like the number 1/3 cannot be cleanly represented in base 10.
Source of the problem:
http://support.microsoft.com/kb/42980
Workarounds:
Is there a definitive solution to javascript floating-point errors?
How to deal with floating point number precision in JavaScript?
http://bytes.com/topic/javascript/answers/682011-solution-floating-point-errors
The way floating point numbers are made, certain values cannot be accurately represented. This is a limitation of this data type, there is little to nothing you can do to fix it, you have to just anticipate this, and make use of round or something.
http://en.wikipedia.org/wiki/Floating_point
Simple rounding errors. floating point numbers are not precise. This makes comparisons a little more complicated. Eg. If (my_float == 3.0) will invariably fail.
To answer your question - floating points have as much precision as your RAM can allow. If you create a floating number 1 - it may actually be 1.000000000000000000001
Obviously your solutions include rounding the number, or using ints